Determine the number of solutions for the given system.

One solution
No solutions
O Intinitelymany solutions

Ask by Fernandez Logan. in the United States

Mar 31,2025

Question

Determine the number of solutions for the given system. $$ y=6 x-\frac{5}{6} $$ $$ y=6 x+5 $$ One solution No solutions O Intinitelymany solutions

UpStudy AI · Accepted Answer

1. Write the equations:
   $$
   y=6x-\frac{5}{6}
   $$
   $$
   y=6x+5
   $$

2. Since the slopes of both equations are $$6$$, the lines are parallel unless they are identical.

3. Compare the $$y$$-intercepts:
   - The first equation has a $$y$$-intercept of $$-\frac{5}{6}$$.
   - The second equation has a $$y$$-intercept of $$5$$.

4. Since $$-\frac{5}{6} \ne 5$$, the lines are distinct and parallel.

5. Therefore, the system has no solutions.

No solutions
The system has no solutions.

Determine the number of solutions for the given system.

One solution
No solutions
O Intinitelymany solutions

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Determine the number of solutions for the given system. One solution No solutions O Intinitelymany solutions